Subgroups — #21419361

Order 7533.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11719687	C₃	1	4	yes	maximal
2	#14578887	C₃	1	8	yes	maximal, complemented
3	C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₃₁	C₃²	1	4	yes	—
6	C₃×C₃₁⋊C₉	C₃²	1	8	yes	—
7	#11719687	—	3	12	no	—
8	C₃²×C₃₁	C₃³	1	1	yes	characteristic
9	C₃×C₃₁⋊C₃	—	3	4	no	—
10	C₉×C₃₁	3₋¹⁺²	1	12	yes	complemented
11	C₃₁⋊C₉	—	3	8	no	—
12	#6900	—	31	1	no	maximal, Sylow
13	C₃×C₃₁	C₃×3₋¹⁺²	1	4	yes	—
14	C₃₁⋊C₃	—	9	1	no	—
15	C₃×3₋¹⁺²	—	31	4	no	—
16	C₉⋊C₉	—	31	8	no	—
17	C₉²	C₃₁⋊C₃	1	1	yes	characteristic, complemented
18	C₃₁	#6900	1	1	yes	characteristic, complemented, Sylow
19	C₃³	—	31	1	no	—
20	3₋¹⁺²	—	93	12	no	—
21	C₃×C₉	—	31	8	no	—
22	C₃×C₉	C₃×C₃₁⋊C₃	1	4	yes	—
23	C₃²	—	93	4	no	—
24	C₃²	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
25	C₉	—	93	8	no	—
26	C₉	#11719687	1	12	yes	complemented
27	C₃	—	279	1	no	—
28	C₃	C₃×#11719687	1	4	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.